A General Method for Approximating Nonlinear Transformations of Probability Distributions

Abstract

In this paper we describe a new approach for generalised nonlinear filtering. We show that the technique is more accurate, more stable, and far easier to implement than an extended Kalman filter. Several examples are provided, including the application of the new filter to problems involving discontinuous functions. 1 Introduction Possibly the most important problem arising in tracking and control applications is the representation and maintenance of uncertainty. The state of a system, whether measured or estimated, is rarely known perfectly because (a) measuring instruments and processes have limited precision, and/or (b) estimates of evolving systems are based on process models that fail to include all governing parameters. The uncertainty associated with a state estimate can be represented most generally by a probability distribution incorporating all knowledge about the state. Because the amount of knowledge about the state is inherently finite, a complete parameterisation of the ..